2 Membrane elements- walls and beams - concrete.ethz.ch€¦ · Idea StatiCa for specific details (corbels, piles caps…) AStrutTie (HanGil) (strut-and-tie fc=? Realistic results?)

2 Membrane elements-walls and beams

09.10.2019 ETH Zurich | Chair of Concrete Structures and Bridge Design | Advanced Structural Concrete 1

2.2 Compatibility-based Stress Fields

Compatibility-based Stress Fields

Overview and nomenclature

09.10.2019 2

2. Membrane elements – walls and beams

2.1 Stress fields (discontinuous or rigid-plastic)

Equilibrium considerations: Lower bound solutions

-- Failure mechanisms (Stahlbeton I)

Kinematic considerations: Upper bound solutions

2.3 Deformation capacity of beams

2.4 Membrane elements: equilibrium & yield conditions

2.5 Membrane elements: load-deformation behaviour

2.2 Compatibility-based Stress Fields

Equilibrium & kinematic considerations:

Exact solutions (simultaneously lower + upper bound)

Tedious hand calculations (iterations,

many load cases)

Digitalisation required!

Concepts only developed for particular elements.

For a general element:

Deformation capacity?

Serviceability checks (deformations, crack widths)?

Computer tool for any element loaded under plane stress

Implements same mechanical concepts

Overcomes the stated limitations

Application to real-life structures

ETH Zurich | Chair of Concrete Structures and Bridge Design | Advanced Structural Concrete


Real-life structures

B Continuity/Bernouilli regions

D Discontinuity regions: static and/or geometric discontinuities are always present

09.10.2019 3

[Tjhin & Kuchma, 2002]



Dimensioning/assesment of real-life structures

B Continuity/Bernouilli regions

• Classic tools (cross sectional analysis): hand calculations feasible; cover all verifications

• Computer-aided tools:

Many available applications for member design: direct implementation of code verifications/mechanical models

D Discontinuity regions

• Classic tools (discontinuous stress fields…): deformation capacity?; serviceability aspects?; hand calculations non-

feasible/productive

• Computer aided-tools:

a) Linear elastic FE-calculations: Non-symmetric strength of concrete only accounted for in the last step (dimensioning

based on yield conditions); unable to predict realistic capacity in existing structures, nor cracking in new ones

b) Non-linear FE-calculations: complex, typically consider tensile strength for equilibrium (differ from classic mechanical

models), code compliant?

c) Gap between a & b for simple but realistic, code-compliant tool, consistent with classic mechanical models

Continuous stress fields = Computer-aided stress fields = Simplified non-linear FE-calculation

09.10.2019 4ETH Zurich | Chair of Concrete Structures and Bridge Design | Advanced Structural Concrete


Dimensioning/assesment of Discontinuity Regions: Existing computer-aided tools

[HanGil, 2017]

Idea StatiCa for specific details

(corbels, piles caps…)

AStrutTie (HanGil) (strut-and-tie fc=? Realistic results?)

[IDEA, 2017]

CAST (Tjhin & Kutchma, 2002)(strut-and-tie fc=? Realistic results?)

[Mata-Falcón & Sánchez-Sevilla, 2006]




09.10.2019 6

Stringer-Panel Models (Nielsen, 1971; Blaauwendraad & Hoogenboom, 1996; Marti & Heinzmann, 2012)

[Blauwendraad, 2006]



Experimental crack pattern

Hand-calculated stress fields

Numerical

results EPSF


[Mata-Falcón, 2015]

[Mata-Falcón et al., 2014]

[Muttoni & Fernandez Ruiz, 2007]

EPSF elastic plastic stress fields (Fernández Ruiz & Muttoni, 2007)

Maintains advantages of hand

calculations (transparent, safe

design with fct = 0, consistent

detailing)

Compressive strength fcdetermined automatically from

strain state

Limited user-friendliness

Limited use for serviceability

… no tension stiffening

… no crack width calculation

No check of deformation

capacity (perfectly plastic

material)



Compatible Stress Field Method (CSFM) - Implemented in commercial software IdeaStatiCa Detail

Continuous stress fields = Computer-aided stress fields

09.10.2019 8

Scope

• Simple method for efficient, code-compliant design and assessment of discontinuity concrete regions

• Including serviceability and deformation capacity verifications

• Direct link to conventional RC design: standard material properties, concrete tensile strength totally neglected for

equilibrium (only its influence to the stiffness is accounted)

Inspirations

• EPSF FE-implementation (strain compatibility, automatic determination of concrete reduction factor from strain state)

• Tension Chord Model TCM and Cracked Membrane Model CMM (tension stiffening, ductility and serviceability checks)

Development / Credits

This project has received partial funding from Eurostars-2

joint programme, with co-funding from the European Union

Horizon 2020 research and innovation programme



CSFM: design process

09.10.2019 9

1) Definition of geometry, loads and load combinations

a) BIM connections: export data from a global model for the analysis of a detail

b) Standalone application:

Full definition

in standalone

user-friendly

application



CSFM: design process

09.10.2019 10

2) Reinforcement design

a) Location of reinforcement: definition by user. Several design tools are provided to identify where the reinforcement is required (for complex regions):

b) Amount of reinforcement: can be automatically designed for all or part of the reinforcement. Not yet released in current version

3) Verification models to check all code requirements

a) Load-bearing capacity

b) Serviceability verifications (deformations, crack width…)

Linear elastic

stress flow

Topological

optimization



CSFM verification model: main assumptions

09.10.2019 11

• AStruTie (HanGil)

based on [Kaufmann and Marti, 1998]

Main assumptions:

• Fictitious rotating-stress-free cracks (σc1,r=0) without slip

• Average strains

• Equilibrium at cracks:

i. Maximum stresses: -σc3,r / σs,r

ii. Concrete tensile strength neglected except for tension-stiffening: εm

Suitable for elements with minimum transversal reinforcement. Slender elements without shear reinforcement might

lead to unconservative results.



CSFM verification model: concrete

09.10.2019 12


Strain limitations of concrete specified by codes

(explicitly considers the increasing brittleness of

concrete with strength).

Imposed to the average strain over a characteristic

crushing band length.

kc discrete values for hand calculations



CSFM verification model: concrete

09.10.2019 13


kc (compression softening) automatically computed based

on the transversal strain state.

Use of fib MC 2010 / SIA 262:213 proposal for shear

verifications (consistent with considered max. stresses)

extended for general cases.

Strain limitations of concrete specified by codes

(explicitly considers the increasing brittleness of

concrete with strength).

Imposed to the average strain over a characteristic

crushing band length.



CSFM verification model: verification of anchorage length and reinforcement

09.10.2019 14

Bond model used exclusively for

anchorage length verifications

Tension-stiffening:

Does not affect the

strength of the

reinforcement

Increases the stiffness

Reduces the ductility

(can reduce the strength

of the member)

explicit failure

criteria *Bilinear naked steel input for design. More

realistic laws for assessment &

experimental validation.

Bare



CSFM verification model: tension stiffening

Stabilized crack pattern

09.10.2019 15

Implementation of

Tension Chord Model

(TCM) [Alvarez, 1998;

Marti et al., 1998]

Average crack spacing:

assumed l=0.67

for r>rcr0.6% Reinforcement is able to

carry the cracking load without yielding0

11sr y ctm

cr

f f n

r




Non-stabilized crack pattern

09.10.2019 16

for r<rcr0.6% Reinforcement is NOT able to carry the cracking load without

yielding. Cracks are controlled by other reinforcement.

Independent cracks are

assumed + bond model of

Tension Chord Model.

Crack localization (size

effect): stiffness of the

whole rebar embedded in

concrete > local stiffness

near the crack

(considered average strain

over lavg).




Resultant tension chord behaviour

09.10.2019 17

Fully cracked behaviour

considered for design.

Uncracked initial stiffness

can be considered for

refined verification

models.



CSFM verification model: effective area of concrete in tension

suitable for numerical implementation and valid for automatic definition of rc,eff in any region

Maximum concrete area each

rebar can activate (concrete at fct)

(illustrated for rebars 3 and 4) Areas used in calculation



CSFM verification model: crack width – stabilized crack pattern

09.10.2019 19

WT4

[Walther, 1967]



CSFM verification model: crack width – non-stabilized crack pattern

09.10.2019 20

[Zhu et al., 2003]

Assumed independent cracks at SLS Considered for:

a) Regions with ρ<0.6%

b) Cracks triggered by geometric discontinuities at low loads

T6



CSFM verification model: crack width – crack kinematic



CSFM & IdeaStatiCa Detail implementation: additional information

Theoretical description of CSFM method & experimental validation

• “Computer-aided stress field analysis of discontinuity concrete regions”, J. Mata-Falcón, D. T. Tran, W. Kaufmann, J. Navrátil; Proceedings of the Conference on Computational Modelling of Concrete and Concrete Structures (EURO-C 2018), 641-650, London: CRC Press, 2018.

https://www.researchgate.net/profile/Jaime_Mata-Falcon/publication/328419485_Computer-aided_stress_field_analysis_of_discontinuity_concrete_regions/links/5bcd7f4da6fdcc03c79ad556/Computer-aided-stress-field-analysis-of-discontinuity-concrete-regions.pdf

Use and installation of Idea StatiCa Detail software:

• Installation of the software: https://www.ideastatica.com/downloads/

Free educational license might be ordered in https://www.ideastatica.com/educational-license/

• Idea StatiCa Resource Center (tutorials, sample projects…): https://resources.ideastatica.com/Content/Home.htm

• Practical workshop will be organised for those students interested


https://www.researchgate.net/profile/Jaime_Mata-Falcon/publication/328419485_Computer-aided_stress_field_analysis_of_discontinuity_concrete_regions/links/5bcd7f4da6fdcc03c79ad556/Computer-aided-stress-field-analysis-of-discontinuity-concrete-regions.pdf

https://www.ideastatica.com/downloads/

https://www.ideastatica.com/educational-license/

https://resources.ideastatica.com/Content/Home.htm


CSFM: practical examples in Idea StatiCa Detail

Deep beam with distributed top load

09.10.2019 23

Problem definition Design of reinforcement


x

z

tF

cF

A

B C

D

E

a

w cqa b f

G

qa

F

q



Deep beam with distributed top load

09.10.2019 24

Compatible stress fields Discontinuous stress fields




Deep beam with distributed load

09.10.2019 25

Top load: fan mechanism Suspended load: arch mechanism

Arch mechanism requires enough capacity of

flexural reinforcement; otherwise, the load is

suspended until top & fan action is generated



CSFM experimental validation

09.10.2019 26

• Direct tension experiments – Alvarez and Marti (1996)

Ultimate limit state

Load deformation behaviour

Crack width

• Pure bending experiments – Frantz and Breen (1978)

Crack width distribution

• Cantilever shear walls – Bimschas, Hannewald and Dazio (2010, 2013)

Load deformation behaviour under combined loading

Bearing capacity under combined loading

• Beams with low amount of transversal reinforcement – Huber, Huber and Kolleger (2016)

Bearing capacity in shear (failures due to insufficient ductility of the transversal reinforcement)




Alvarez and Marti (1996) - experimental setup/specimens

09.10.2019 27

[Avarez and Marti, 1996]

Z1 Z1

Specimen Z1 Z2 Z4 Z8

Long.

reinforcement

14xØ14

(ρ = 1%)

14xØ14

(ρ = 1%)

14xØ14

(ρ = 1%)

10xØ14

(ρ = 0.7%)

Steel quality

(ductility class)High High Normal High

fck_cube (MPa) 50 90 50 50

Loading: pure tension




Alvarez and Marti (1996) - ultimate state

09.10.2019 28

[Avarez and Marti, 1996]

Specimen Z1 Z2 Z4 Z8

Experiment

Vexp (kN)

εm,exp (%)

1294

6.7

1295

6.8

1275

0.6

924

6.4

CSFM

Vcalc (kN)

εm,calc (%)

1275

7.0

1282

4.6

1242

0.4

918

6.5

Safety factor

Strength: Vexp/Vcalc

Deform. capacity: εm,exp/εm,calc

1.01

0.96

1.01

1.48

1.03

1.50

1.01

0.98

V: Peak load

εm: Average tensile strain




Alvarez and Marti (1996)

Load deformation behaviour

09.10.2019 29

Neglecting tension-stiffening

overestimates the deformation

capacity up to 5 times

(depending on ρ, the ductility of

the reinforcement…)




Alvarez and Marti (1996) -

crack width


Computergestützte Spannungsfelder


Frantz and Breen (1980) - experimental setup/specimen

09.10.2019 31


Specimen RS-3

Main reinforcement

2xØ15.886xØ12.7

Web reinforcement

6xØ6

Loading: pure bending

[Frantz and Breen, 1980]

d (mm)

885 mm




Frantz and Breen (1980) – crack width




Bimschas et al. (2010, 2013) – experimental setup/specimens

09.10.2019 33

VK1: first yielding of

reinforcement[Bimschas, 2010]

1370 kN

±V

Specimen VK1 VK3 VK6

Effective height

(m) 3.30 3.30 4.50

Section depth (m) 1.50 1.50 1.50

Section width (m) 0.35 0.35 0.35

ρsl (%) 0.82 1.23 1.23

ρst (%) 0.08 0.08 0.08

Loading: constant normal force N = -1370kN; quasi-static cyclic

loading with increasing amplitudes in horizontal direction.

Note: CSFM aim at describing the backbone of the cyclic response

using a monotonic model. Strain penetration into the foundation is

not considered.

eu=8.4%




Bimschas et al. (2010, 2013) – peak load

09.10.2019 34

[Bimschas, 2010]

VK1: peak strength VK1: failure

Concrete crushing in

compression

Specimen VK1 VK3 VK6

Experiment*

Vexp (kN)728 876 647

CSFM

Vcalc(kN)730 860 650

Vexp/Vcalc 1.00 1.02 1.00

Note: CSFM aims at describing the

behaviour of the backbone until concrete

peak horizontal strength is reached, (≠ to

loss of vertical bearing capacity).

*mean peak horizontal load of North and

South directions.




Bimschas et al. (2010, 2013) – load deformation behaviour

09.10.2019 35

Failure mode: concrete crushing in compression. Failure is considered when the strain limit criteria specified in codes for sectional

analysis is reached on average over the crushing band length.




Bimschas et al. (2010, 2013) – stress fields specimen VK1

09.10.2019 36

Note: Refined analysis considers the initial uncracked stiffness, as well as the actual stress-strain relationship of the

reinforcement. Moreover, no concrete strain limitation is considered.


Compatibility-based Stress FieldsCSFM experimental validation: Bimschas et al. (2010, 2013) – load deformation behaviour

09.10.2019 37

[%]

sr/ft

c3r/(fc·kc)

sr>fy1370 kN

250 kN

84º

1370 kN

500 kN

80º

1370 kN

750 kN

79º

sr<0




Huber et al. (2016) – experimental setup/specimens

09.10.2019 38

Øw(mm)

fy(MPa)

ft(MPa)

eu(%)

4 653 710 4.9

6 569 658 3.1

12 552 654 3.4

Specimen R1000m35 R1000m60 R500m352 R500m351

Section depth 1.00 m 1.00 m 0.50 m 0.50 m

Section width 0.30 m 0.30 m 0.15 m 0.15 m

rw0.094 % 0.094 % 0.084 % 0.094 %

ØwØ6 Ø12 Ø4 Ø6

fc 29.6 MPa 60.9 MPa 35.9 MPa 37.9 MPa




Huber et al. (2016) – ultimate load

09.10.2019 39

• Neglecting tension stiffening leads to unsafe load predictions and does not capture the real failure mode (stirrup rupture).

• Higher impact of strain localization in real size elements use of existing experimental databases could underestimate the impact of these failures.

Cold-formed steel with same ft & fy less ductile & less

predicted load (≈10%) than standard bilinear steel law.

CSFM CSFM

CSFM

CSFM




Huber et al. (2016) – stress fields specimen R1000m35

09.10.2019 40

776 kN

q=40.5º

937 kNStirrups yielding

q=36.5º

ez=20‰ 0‰

srz=600 MPa<ft

e1=23‰ kc=0.41

c3r=12 MPa

c3r/(fc·kc)=1.00

ez=5.4‰

srz=638 MPa=ft

e1=6.4‰ kc=0.64

c3r=7.7 MPa

c3r/(fc·kc)=0.42

*Results at the most restrictive

concrete and steel finite elements

(minimum kc & maximum srz)

CSFM (No tens.-stiff.)

CSFM

[%]

sr/ft

c3r/(fc·kc)

sr>fy


Documents

2 Membrane elements- walls and beams - concrete.ethz.ch€¦ · Idea StatiCa for specific details (corbels, piles caps…) AStrutTie (HanGil) (strut-and-tie fc=? Realistic results?)